I can confirm that the thing with the red hands is definitely a power effect. You can see Shulk uses the down smash on Ganondorf early on and it does very little knockback, but then later on, with Ganondorf taking no more damage between the two attacks, Shulk hits him again with the down smash while having the red hands activated and it sends Ganondorf flying much further.
A little criticism though: I think the mode that activates the power effect is Monado Enchant. It makes more sense than Monado Buster since along with allowing people to hurt mechon is also improves the damage of auto attacks. You show that both of them are in use in the video, but it does not really make sense that both of them boost power, since Monado Enchant's mode wouldn't make sense to do anything else.
When the mode deactivates, it doesn't really look like Monado Buster to me in that frame that was paused. It's hard to make it out to be anything rally, but a few frames later, you have Monado Enchant.
If it is Monado Enchant, that explains the difference in order you bring up in the video.
I enjoyed the video though, really nice analysis
edit: Oh and I love the music too! I'm a big fan of the Colony 9 music